- The Purpose Of A Ballistic Pendulum Is To Measure The Velocity Of A Projectile Using The Principle Of Conservation Of Mo 1 (74.8 KiB) Viewed 32 times
be used to verify the results from this experiment. How can one
check how well the aim of this experiment was satisfied?
The purpose of a ballistic pendulum is to measure the velocity of a projectile using the principle of conservation of momentum during a perfectly inelastic collision. Simple theory from early in the course is outlined in Fig. 1: ө L L v=0 Vp1 = ? Ah! m M v M+m (2) Just after collision (1) Just before collision (3) Maximum swing Fig. 1 Simple theory of a ballistic pendulum: Point masses - momentum is conserved from (1) to (2) and mechanical energy is conserved from (2) to (3). The masses are treated as points. Rotational kinetic energy is not considered.
For the method shown in Fig. 1, , 0, m and M are measured and vp1 is calculated working backwards from state (3) to state (2) and then from state (2) to state (1). If the mass of the rod connecting the mass M to the pivot point is not negligible, a slightly more accurate method is to treat the pendulum as a rigid body as shown in Fig. 2. String loop One RE Find centre of mass Angular momentum = m2 (with respect to 0) Angular momentum = 1 (with respect to O) L RG RG m Kinetic energy = 12 (2) Just after collision (1) Just before collision (3) Maximum swing Fig. 2 More complete theory of a ballistic pendulum: Rotating rigid body - angular momentum is conserved from (1) to (2) and mechanical energy is conserved from (2) to (3) To use the method in Fig. 2, we need to know the mass moment of inertia about 0 of the pendulum (1.). This can be found by measuring the time period of the pendulum swinging using the following equation: MotORGE lo = (1) 42 Where Meat is the total mass of the pendulum (including the embedded projectile), g is the acceleration due to gravity Rg is the position of the centre of mass with respect to the pivot 0, and t is the time period of the free swing.